Analysis of thermoacoustic instabilities were dominated by modal (eigenvalue) analysis for many decades. Recent progress in nonmodal stability analysis allows us to study the problem from a different perspective, by quantitatively describing the short-term behavior of disturbances. The short term evolution has a bearing on subcritical transition to instability, known popularly as triggering instability in thermoacoustic parlance. We provide a review of the recent developments in the context of

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... riggering instability. A tutorial for non-modal stability analysis is provided. The applicability of the tools from non-modal stability analysis are demonstrated with the help of a simple model of a Rjike tube. The paper closes with a brief description of how to characterize bifurcations in thermoacoustic systems.